Calculation of antiphase boundaries on {110} planes in a b2 ordered compound by the cluster variation method

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Abstract
Antiphase boundaries (APBs) on {110} planes in a stoichiometric AB compound with the B2 ordered structure have been investigated using the cluster variation method. The basic irregular tetrahedron of the b.c.c. lattice is chosen as the maximum cluster for the entropy approximation, and the ordering energy of nearest-neighbour pairs is employed to evaluate the internal energy. The excess free energy due to the APB shows a monotonic decrease with increasing temperature and vanishes at T c as it should, considering that the B2↔disorder transition is second order. The excess internal energy exhibits a maximum at around 0.7T c before vanishing at T c. Up to about 0.3T c, the APB structure keeps the sharp profile of the pure shear structure at 0 K. Then it locally disorders and widens, the profile becoming flat and infinitely wide at T c. At each temperature, there exists a number of equilibrium APB configurations with almost the same energies corresponding to the same APB but located at different positions along the APB normal. The calculated APB structures are used to evaluate, as a function of temperature, the stress necessary to move a superdislocation dissociated into two ½ superpartials bounding an APB. On the leading partial the stress is almost proportional to the long-range order parameter of the homogeneous system, which decreases monotonically from 0 K to T c. On the trailing partial, the stress is proportional to minus the degree of order existing locally at the boundary. This quantity shows a sharp increase between 0.3 T c and 0.6T c so that the resulting stress on the superpartial due to the diffuse APB reaches a maximum at about 0.65T c. Comparison with the critical resolved shear stress peak in β-brass shows excellent agreement in terms of peak temperatures, the calculated stress at the peak being about three times the experimental value. This difference is discussed considering the competition between the dynamics of APB profile widening by diffusion and that of dislocation motion.

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